Characterization of the automorphisms having the lifting property in the category of abelian p‐groups

Let p be a prime. It is shown that an automorphism α of an abelian p‐group A lifts to any abelian p‐group of which A is a homomorphic image if and only if α = π idA, with π an invertible p‐adic integer. It is also shown that if A is torsion group or torsion‐free p‐divisible group, then idA and −idA are the only automorphisms of A which possess the lifting property in the category of abelian groups.